Art isn't easy, as a famous creator of musicals once wrote, but it almost always involves big ideas. In Michael Kramer and D. S. Moynihan's play, Divine Rivalry, playing through August 5 at San Diego's Old Globe, there's lots of proof of the difficulty of creation and not nearly enough big ideas.

Starting with a little-known historical incident, the play follows a familiar dramatic course: bring two geniuses with big egos into the same space, and let them duke it out verbally. All well and good, except that Divine Rivalry is actually not so fascinated with its two geniuses, Leonardo da Vinci (Miles Anderson) and Michelangelo Buonarroti (Euan Morton), as it is with a genius-in-training, Niccolò Machiavelli (Sean Lyons).

In a time when Italy functioned as a set of city-states, military skirmishes flourished and territory was difficult to defend. Florence had made a name for itself as a city that valued art, though that value had been suppressed under the Puritanical rule of Girolamo Savonarola, who had succeeded the Medici family as ruler. When Savonarola, a priest, was excommunicated and then burned at the stake following a power struggle with the Pope, there was an opportunity to restore Florence as an art center. Michelangelo, a young upstart who had worked mostly in Rome, caused a stir when his nude sculpture of the Biblical King David was unveiled in a prominent location, and Machiavelli, who was a deputy to the current leader Piero Soderini (David Selby), may well have persuaded his boss to invite Michelangelo and Leonardo da Vinci, Florence's leading Renaissance master, to carry the competition that had arisen between them into painting two wall sections in the same room.

It's a great idea for a play, but it goes awry when Mr. Kramer, a political journalist, becomes more interested in the politics of urban planning than in art. Machiavelli has trouble persuading Soderini to pursue the joint commissions because his plan to reroute Florence's Arno River was an expensive failure. And when he does manage to obtain approval to proceed, the act one storyline focuses on what Machiavelli tells or doesn't tell to each of the players as he pursues a sort of shuttle diplomacy that comes across as, well, Machiavellian (though, the script actually uses that word in dialogue, a major gaffe, as Machiavelli was at this time nowhere near famous enough for such usage).

Act two gets the artists into the same room, where they grudgingly talk to each other. Most of the talk revolves around missed opportunities in each artist's previous works, and while most of these works may be familiar to audiences, the text makes a lot of assumptions about what the audience already knows (the Globe has helpfully provided multiple essays in its program to bridge the gap, but taken together they constitute a lot of reading to be done before the curtain rises). Once the egos have been pierced, though, it turns out that there is some grudging respect between the two artists.

Mostly missed are hints that the artists are aware of the social and political milieu in which they function. There could have been discussions of the role of patrons (the Medicis, the church, the state itself) in the artistic process, or of the tensions between science (as pursued vigorously by Leonardo) and religious fundamentalism (a hallmark of the Savonarola regime). There could have been interesting discussions of the role of sexuality in art and politics (scholars think all three principals were gay or bisexual, albeit they also think that the three were mostly celibate). Mr. Kramer's script (Ms. Moynihan came along after the play's world premiere production at the Hartford Stage) touches lightly and sometimes confusingly on these topics but doesn't pursue them.

Michael Wilson, the former artistic director at the Hartford Stage, recognizes some of these deficiencies and attempts to cover them with personnel and production choices. He has cast Mr. Anderson, a Globe favorite and expert scene-chewer, in the showier role of Leonardo, and consequently Mr. Morton more or less disappears into the role of the younger artist. Jeffrey Carlson, Mr. Morton's cast mate in the musical Taboo, was announced to play Machiavelli, and it would have been interesting to watch how their chemistry from that production carried into this one. But, Mr. Carlson withdrew shortly before previews began, and Mr. Lyons doesn't bring any of that history to the role.

Prominent in the production is John Gromada's original music and sound design, both reminiscent of the days when the Globe's Conrad Susa would use loud and bombastic compositions to make the stage action seem more significant than was actually the case. Projection designer Peter Nigrini, whose eye-popping work was the best thing about the La Jolla Playhouse production of Sleeping Beauty Wakes, touches this production in the same magical ways, allowing the audience to get glimpses of the art that the performers are discussing.

It's too bad there are so many missed opportunities in the script, though the advantage is that audience members will have a lot to discuss on the ride home as they try to figure out what they've just seen.

Performs through August 5, 2012, on the Donald and Darlene Shiley Stage at the Old Globe campus, 1363 Old Globe Way, in San Diego's Balboa Park. Tickets ($29 - $92) are available at the box office, by calling (619) 23-GLOBE, or by visiting the Old Globe's website, at theoldglobe.org.